Use the same thumbprint on every org and control access using the SAML Roles
User 1 gets group "Org Type 1 Admin"
User 2 gets group "Org Type 2 Admin"
Org 1 has "Org Type 1 Admin" on it as a role and does NOT have "Org Type 2 Admin"
Org 2 has "Org Type 2 Admin" on it as a role and does NOT have "Org Type 1 Admin" on it as a role.
User 1 will get access just to org 1, User 2 will get access just to org 2. The thumbprint must match AND there must be a matching role to grant access on the org.